How Does Magnetism Work in Different Scenarios?

[James2911]

Hi. I have three questionns to ask.

1. A very close point on the axis foo a current carrying circular coil (x<<<R) of radius R, the value of magnetic field decreases by a fraction of 5% with respect to the center value. The position of the point from the center of the coil is:

(a) R/10^1/2
(b) R/30^1/2
(C) R/50^1/2
(d) R/150^1/2

2. A charge +2q moves vertically upwards with speed v, a second charge -q moves horizontally to the right with the same speed v, and a third charge +q moves horizontal to the right with the same speed v. The point P is located a perpendicular distance a away from each charge as shown in the figure. The magnetic field at P is ..

Here’s the diagram:

-q ----------> v
|
| ^ v
| |
| |
. P ----------o +2q
|
|
|
o---------> v (+q)

Answer is :
Out of the page with magnitude u(naught) 4qv/4pia^2

1. The equation of line on which magnetic field is zero due to system of two perpendicular infinitely long current carryng straight wire is :-

^ +Y axis
|
| (current flowing thru here is 3I)
|
|
---------------------------------------------------------> x
| (current flowing in +x is I)
|
|The answer is x=3y

Since the above 2 diagrams might not be clear, I am uploading screenshots for the same.1. I tried the first question thinking as a Bionomial expression, and getting x = .794R which is not even in the option.

2.I've always solved problems in which only a wire is involved, either square, triangle, straight shapes. But not charges. Do we apply Biot Savart law here? I am able to determine the direction of the magnetic field via knocking rule but have completely no idea about the magnitude.

3. I am guessing, since we want it to be zero, we will place it on X axis first, so that the field due to itself is zero and then at a distance of 3y it will be zero from the y-axis as well or so.

Any help would be appreciated!

 

[jbsteele]

For the first question, you can use the formula B=μ₀/(2πr) to calculate the magnetic field of the coil at a given distance from the center. This will tell you how much the field has decreased by a fraction of 5%. For the second question, you can use Biot-Savart's Law to calculate the magnetic field due to each of the charges. You will need to add the fields together to get the total magnetic field at point P.For the third question, you can use the principle of superposition to calculate the total magnetic field due to both the current-carrying wires. The equation of the line on which the magnetic field is zero will be the sum of the equations of the lines on which the magnetic field from each wire is zero.